首页|On a rigidity condition for Berwald spaces

On a rigidity condition for Berwald spaces

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We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if (M, F) is a Finsler structure such that there exists a Riemannian structure that leaves invariant the indicatrix under parallel transport of the associated Levi-Civita connection, then the structure (M, F) is Berwald. As application, a necessary condition for pure Landsberg spaces is formulated. Using this criterion we provide an strategy to solve the existence or not of pure Landsberg surfaces.

berwald spacefinsler structurelandsberg spaceaverage of a linear connection

Ricardo Gallego Torrome、Fernando Etayo

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Department of Physics, Lancaster University, Lancaster, LA1 4YB, & The Cockcroft Institute, UK, United Kingdom

Departamento de Matematicas, Estadistica y Computation, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s/n, 39071 Santander, Spain

2010

10.5052/RACSAM.2010.07

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A. Matematicas

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Serie A. Matematicas

ISSN：1137-2141
年,卷(期)：2010.104(1)
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